Bottom Line:
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H.Yuen and J.In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

ABSTRACTWe reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

f1: Schematics for homodyne and heterodyne detections.In our context, the heterodyne scheme shall be understood as a double-homodyne scheme (shown in (b)) that measures two complementary sets of quadrature eigenstates (those of position X and momentum P) simultaneously.

Mentions:
It therefore goes without saying that quantum tomography techniques for quantum states of light are of major interest in recent years. One of the most popular techniques, quantum homodyne detection232425, is used in quantum optics to measure intensities of light signals from the outputs of a beam splitter that coherently merges the light mode from the source and that from a local oscillator, or reference coherent state. The result is an approximate measurement of the eigenstates of a rotated photonic quadrature whose phase angle depends on the phase of the local oscillator. The homodyne data obtained per binned angle constitute a distribution of points along a particular phase-space cut defined by this angle. This distribution is precisely the marginal distribution of the Wigner function of the quantum state of the source over the complementary quadrature. There is another well-known optical technique, heterodyne detection2627282930313233, which has been extensively used to simultaneously probe a pair of optical beams of different frequencies in order to measure their relative phase. Compared to quantum homodyne detection, there are apparently relatively fewer published works on using its quantum variant to perform quantum tomography. This involves simultaneously measuring signal intensities of beams that are split from a single source signal by a beam splitter, thus realizing the approximate measurement of two rotated quadratures (position and momentum say) that are complementary to each other (see Fig. 1 for schematics). Because of the nature of such a quantum measurement, we shall understand the heterodyne scheme discussed here as a quantum double-homodyne tomography scheme, and henceforth, with common understanding, drop the adjective “quantum” when referring to these schemes. The heterodyne data obtained constitute a distribution of points according to the Husimi Q function of the state.

f1: Schematics for homodyne and heterodyne detections.In our context, the heterodyne scheme shall be understood as a double-homodyne scheme (shown in (b)) that measures two complementary sets of quadrature eigenstates (those of position X and momentum P) simultaneously.

Mentions:
It therefore goes without saying that quantum tomography techniques for quantum states of light are of major interest in recent years. One of the most popular techniques, quantum homodyne detection232425, is used in quantum optics to measure intensities of light signals from the outputs of a beam splitter that coherently merges the light mode from the source and that from a local oscillator, or reference coherent state. The result is an approximate measurement of the eigenstates of a rotated photonic quadrature whose phase angle depends on the phase of the local oscillator. The homodyne data obtained per binned angle constitute a distribution of points along a particular phase-space cut defined by this angle. This distribution is precisely the marginal distribution of the Wigner function of the quantum state of the source over the complementary quadrature. There is another well-known optical technique, heterodyne detection2627282930313233, which has been extensively used to simultaneously probe a pair of optical beams of different frequencies in order to measure their relative phase. Compared to quantum homodyne detection, there are apparently relatively fewer published works on using its quantum variant to perform quantum tomography. This involves simultaneously measuring signal intensities of beams that are split from a single source signal by a beam splitter, thus realizing the approximate measurement of two rotated quadratures (position and momentum say) that are complementary to each other (see Fig. 1 for schematics). Because of the nature of such a quantum measurement, we shall understand the heterodyne scheme discussed here as a quantum double-homodyne tomography scheme, and henceforth, with common understanding, drop the adjective “quantum” when referring to these schemes. The heterodyne data obtained constitute a distribution of points according to the Husimi Q function of the state.

Bottom Line:
We reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H.Yuen and J.In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.

ABSTRACTWe reveal that quadrature squeezing can result in significantly better quantum-estimation performance with quantum heterodyne detection (of H. P. Yuen and J. H. Shapiro) as compared to quantum homodyne detection for Gaussian states, which touches an important aspect in the foundational understanding of these two schemes. Taking single-mode Gaussian states as examples, we show analytically that the competition between the errors incurred during tomogram processing in homodyne detection and the Arthurs-Kelly uncertainties arising from simultaneous incompatible quadrature measurements in heterodyne detection can often lead to the latter giving more accurate estimates. This observation is also partly a manifestation of a fundamental relationship between the respective data uncertainties for the two schemes. In this sense, quadrature squeezing can be used to overcome intrinsic quantum-measurement uncertainties in heterodyne detection.